Question: Simplify the following expression: $ p = \dfrac{3}{7} + \dfrac{k - 8}{-6k + 10} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6k + 10}{-6k + 10}$ $ \dfrac{3}{7} \times \dfrac{-6k + 10}{-6k + 10} = \dfrac{-18k + 30}{-42k + 70} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{k - 8}{-6k + 10} \times \dfrac{7}{7} = \dfrac{7k - 56}{-42k + 70} $ Therefore $ p = \dfrac{-18k + 30}{-42k + 70} + \dfrac{7k - 56}{-42k + 70} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{-18k + 30 + 7k - 56}{-42k + 70} $ $p = \dfrac{-11k - 26}{-42k + 70}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{11k + 26}{42k - 70}$